Problem: Simplify the following expression: $ k = \dfrac{-2x}{x - 3} - \dfrac{9}{2} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{2}{2}$ $ \dfrac{-2x}{x - 3} \times \dfrac{2}{2} = \dfrac{-4x}{2x - 6} $ Multiply the second expression by $\dfrac{x - 3}{x - 3}$ $ \dfrac{9}{2} \times \dfrac{x - 3}{x - 3} = \dfrac{9x - 27}{2x - 6} $ Therefore $ k = \dfrac{-4x}{2x - 6} - \dfrac{9x - 27}{2x - 6} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{-4x - (9x - 27) }{2x - 6} $ Distribute the negative sign: $k = \dfrac{-4x - 9x + 27}{2x - 6}$ $k = \dfrac{-13x + 27}{2x - 6}$